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A unit spherical Euclidean distance matrix (EDM) D is a matrix whose entriescan be realized as the interpoint (squared) Euclidean distances of n points ona unit sphere. In this paper, given such a D and 1 \leq k < l \leq n, wepresent a characterization of the set of all unit spherical EDMs whose entriesagree with those of D except possibly with the entry in the klth and lkthpositions. As a result, we show that this set can be discrete, consisting ofone or two elements, or it can be continuous. The results are derived using twoalternative approaches, the second of which is based on Cayley-Menger matrices.

On Unit Spherical Euclidean Distance Matrices Which Differ in One Entry